Homotopy triangulations of a manifold triple
Rolando Jiménez and Yuri M. Muranov

The set of homotopy triangulations of a given manifold fits into a surgery exact sequence which is the main tool for the classification of manifolds. In the present paper we describe relations between homotopy triangulations of different manifolds for a given manifold triple and its connection to surgery theory. We introduce a group of obstructions to split a homotopy equivalence along a pair of submanifolds and study its properties. The main results are given by commutative diagrams of exact sequences.

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